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Problem in set theory
In mathematics, Suslin's problem is a question about totally ordered sets posed by Mikhail Yakovlevich Suslin (1920) and published posthumously. It has
Suslin's_problem
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Russian mathematician
Institute. Suslin died of typhus in the 1919 Moscow epidemic following the Russian Civil War, at the age of 24. His name is associated to Suslin's problem, a
Mikhail_Suslin
Intersection of Set Theory and General Topology
questions that can be solved using set-theoretic methods, for example, Suslin's problem. In the mathematical field of general topology, a Dowker space is a
Set-theoretic_topology
Surname list
new Suslin sets Suslin operation Suslin's problem Suslin representation, a set of real numbers built up in a certain way Sergey Suslin (1944–1989), Soviet
Suslin
Mathematical tree
ℵ2-Suslin tree, is a longstanding open problem. Glossary of set theory Kurepa tree List of statements independent of ZFC List of unsolved problems in
Suslin_tree
German logician and mathematician (1871–1953)
theory. Proposed in 1931, Zermelo's navigation problem is a classic optimal control problem. The problem deals with a boat navigating on a body of water
Ernst_Zermelo
Proposition in mathematical logic
problems in set theory, and establishing its truth or falsehood was the first of Hilbert's 23 problems presented in 1900. The answer to this problem is
Continuum_hypothesis
Set with exactly one element
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Singleton_(mathematics)
Paradox in set theory
Gottlob Frege of the paradox in Frege's 1879 Begriffsschrift and framed the problem in terms of both logic and set theory, and in particular in terms of Frege's
Russell's_paradox
German mathematician (1831–1916)
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Richard_Dedekind
Pair of logical equivalences
are especially useful when simplifying logical expressions in proofs and problem solving. The laws are named after Augustus De Morgan (1806–1871), who introduced
De_Morgan's_laws
Proof by Alan Turing
infallibly gives a correct "yes" or "no" answer to each instance of the problem. In Turing's own words: "what I shall prove is quite different from the
Turing's_proof
Branch of mathematics that studies sets
independent of ZFC, requiring stronger axioms for their proof. A famous problem is the normal Moore space question, a question in general topology that
Set_theory
Any one of the distinct objects that make up a set in set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Element_of_a_set
Condition in order theory and topology
non-empty open subsets of X is countable. The name originates from Suslin's Problem. Every separable topological space has the ccc. Furthermore, a product
Countable_chain_condition
Use of braces for specifying sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Set-builder_notation
Set of the elements not in a given subset
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Complement_(set_theory)
The real numbers or their cardinality
axioms characterize the order type of the real number line. Aleph null Suslin's problem Transfinite number Weisstein, Eric W. "Continuum". mathworld.wolfram
Continuum_(set_theory)
Generalization of "n-th" to infinite cases
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Ordinal_number
Standard system of axiomatic set theory
hypothesis and the negation of the Suslin hypothesis. Martin's axiom plus the negation of the continuum hypothesis implies the Suslin hypothesis. The constructible
Zermelo–Fraenkel_set_theory
Concept in axiomatic set theory
Press, 0-674-55451-5 Toth, Gabor (2021-09-23). Elements of Mathematics: A Problem-Centered Approach to History and Foundations. Springer Nature. p. 32.
Axiom_schema_of_specification
Sets whose elements have degrees of membership
"Named Sets in the Analysis of Uncertainty". Methodological and Theoretical Problems of Mathematics and Information Sciences. Kiev: 72–85. Cattaneo, Gianpiero;
Fuzzy_set
Axiom of set theory
} has a model. Unsolved problem in mathematics Does the partition principle imply the axiom of choice? More unsolved problems in mathematics There are
Axiom_of_choice
Mathematics textbook
axioms, and quickly develops combinatorial notions such as trees, Suslin's problem, the diamond principle, and Martin's axiom. It develops some basic
Set Theory: An Introduction to Independence Proofs
Set_Theory:_An_Introduction_to_Independence_Proofs
Mathematical concept
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Transfinite_induction
Mathematical logician and philosopher
Mathematical Logic), an introduction to first-order logic in which the problem of completeness was posed: "Are the axioms of a formal system sufficient
Kurt_Gödel
Mathematical set containing no elements
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Empty_set
Mathematical concept
Mathematical Reasoning, MacMillan D'Angelo; West (2000), Mathematical Thinking: Problem Solving and Proofs, Prentice Hall Cupillari, The Nuts and Bolts of Proofs
Equivalence_class
Finite ordered list of elements
preprint D'Angelo, John P.; West, Douglas B. (2000), Mathematical Thinking/Problem-Solving and Proofs (2nd ed.), Prentice-Hall, ISBN 978-0-13-014412-6 Keith
Tuple
American philosopher and logician (1908–2000)
The problem of non-referring names is an old puzzle in philosophy, which Quine captured when he wrote, A curious thing about the ontological problem is
Willard_Van_Orman_Quine
English philosopher and logician (1872–1970)
Unwin 1921. The Analysis of Mind. London: George Allen & Unwin 1922. The Problem of China. London: George Allen & Unwin 1922. Free Thought and Official
Bertrand_Russell
3-volume treatise on mathematics, 1910–1913
established for Principia's axioms of set theory. (See Hilbert's second problem.) Russell and Whitehead suspected that the system in PM is incomplete:
Principia_Mathematica
Mathematical set formed from two given sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Cartesian_product
Axiom of set theory proposed by Peter Aczel in 1988
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Aczel's_anti-foundation_axiom
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Nested_set_collection
Mathematician (1845–1918)
function by trigonometric series. Cantor solved this problem in 1869. It was while working on this problem that he discovered transfinite ordinals, which occurred
Georg_Cantor
Ultrafilter lemma Tree (set theory) Tree (descriptive set theory) Suslin's problem Absorption law Prewellordering Stone duality Stone's representation
List_of_order_theory_topics
Complement (set theory) Complete Boolean algebra Continuum (set theory) Suslin's problem Continuum hypothesis Countable set Descriptive set theory Analytic
List_of_set_theory_topics
Possible axiom for set theory
initial ordinals, and we have δ1 2n+2 = (δ1 2n+1)+, and for n < ω, the 2n-th Suslin cardinal is equal to δ1 2n−1. AD+ Axiom of real determinacy (ADR) Borel
Axiom_of_determinacy
American mathematician
having never published a proof of it, Tennenbaum had also studied Suslin's problem and computably enumerable sets. Over his academic career in the 1960s
Stanley_Tennenbaum
Elements in exactly one of two sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Symmetric_difference
Branch of mathematics
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Order_theory
Term in set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Almost
Commutative algebra theorem
The Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra concerning the relationship between
Quillen–Suslin_theorem
Every set is smaller than its power set
some natural number, say b {\displaystyle b} . However, this causes a problem. If b {\displaystyle b} is in B {\displaystyle B} , then b {\displaystyle
Cantor's_theorem
Basic framework of mathematics
(multivariable polynomial equation) has a solution in integers. 1971: Suslin's problem is proven to be independent from ZFC. Starting in 1935, the Bourbaki
Foundations_of_mathematics
American mathematician (1934–2007)
locally compact group is the convolution of two such functions, solving a problem posed by Walter Rudin. In Cohen (1960), he made a significant breakthrough
Paul_Cohen
Czech mathematician
gave the first published proof of the consistency of the existence of a Suslin line. With Karel Prikry, he introduced the notion of precipitous ideal.
Thomas_Jech
Axiom used in set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Axiom_of_extensionality
Collection of mathematical objects
characterized by the formula. There are several ways for avoiding the problem. One may prove that the formula defines a set; this is often almost immediate
Set_(mathematics)
Alternative to the standard Zermelo–Fraenkel set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
List of alternative set theories
List_of_alternative_set_theories
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Generic_filter
Particular class of sets which can be described entirely in terms of simpler sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Constructible_universe
Order whose elements are all comparable
total partial order Ranking – Relationship between items in a set Suslin's problem – Problem in set theory Well-order – Class of mathematical orderings Let
Total_order
One-to-one correspondence
Chapman & Hall/ CRC Press. D'Angelo; West (2000). Mathematical Thinking: Problem Solving and Proofs. Prentice Hall. Cupillari (1989). The Nuts and Bolts
Bijection
Concept in axiomatic set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Axiom_of_power_set
Set theory concept
1996 by Oxford University Press, New York]. Set Theory and the Continuum Problem. Dover. ISBN 978-0-486-47484-7. von Neumann, John (1923). "Zur Einführung
Von_Neumann_universe
Proof in set theory
For example, the conventional proof of the unsolvability of the halting problem is essentially a diagonal argument. Also, diagonalization was originally
Cantor's_diagonal_argument
Pair of mathematical objects
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Ordered_pair
Mathematical set that can be enumerated
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Countable_set
Complement (set theory) Complete Boolean algebra Continuum (set theory) Suslin's problem Continuum hypothesis Countable set Descriptive set theory Analytic
List of mathematical logic topics
List_of_mathematical_logic_topics
Set of elements in any of some sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Union_(set_theory)
Set whose elements all belong to another set
displaying short descriptions of redirect targets Subset sum problem – Decision problem in computer science Subsumptive containment – System of elements
Subset
Infinite set that is not countable
_{1}} . In 1900, David Hilbert posed this question as the first of his 23 problems. The statement that ℵ 1 = ℶ 1 {\displaystyle \aleph _{1}=\beth _{1}} is
Uncountable_set
\aleph _{1}} -dense sets are order-isomorphic is independent of ZFC. Suslin's problem asks whether a specific short list of properties characterizes the
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
In mathematics, operation on sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Disjoint_union
Mathematical concept for comparing objects
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Equivalence_relation
Collection of sets in mathematics that can be defined based on a property of its members
Smullyan, Raymond M.; Fitting, Melvin (2010), Set Theory And The Continuum Problem, Dover Publications, ISBN 978-0-486-47484-7 Monk, Donald J. (1969), Introduction
Class_(set_theory)
Finite sets whose elements are all hereditarily finite sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Hereditarily_finite_set
Concept in topology
space, a subset is a Suslin space if and only if it is a Suslin set (an image of the Suslin operation). The following are Suslin spaces: closed or open
Polish_space
Type of cardinal number in mathematics
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Regular_cardinal
Diagram that shows all possible logical relations between a collection of sets
supplemental rules for the standard Venn diagram, in order to account for certain problem cases. For instance, regarding the issue of representing singular statements
Venn_diagram
Set of elements common to all of some sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Intersection_(set_theory)
Theorem in set theory
Klein; Walther von Dyck; David Hilbert; Otto Blumenthal (eds.), "Über das Problem der Wohlordnung", Mathematische Annalen (in German), 76 (4): 438–443, doi:10
Schröder–Bernstein_theorem
Family of subsets representing "large" sets
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Filter_on_a_set
Mathematical construction of a set with an equivalence relation
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Setoid
Mathematical set of all subsets of a set
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Power_set
Size of a possibly infinite set
Klein; Walther von Dyck; David Hilbert; Otto Blumenthal (eds.), "Über das Problem der Wohlordnung", Math. Ann., Bd. 76 (4), Leipzig: B. G. Teubner: 438–443
Cardinal_number
American logician (1943–2011)
Hampshire. The mathematical context in which Baumgartner worked spans Suslin's problem, Ramsey theory, uncountable order types, disjoint refinements, almost
James_Earl_Baumgartner
Line formed by the real numbers
nonempty open intervals in R is countable. In order theory, the famous Suslin problem asks whether every linear continuum satisfying the countable chain condition
Number_line
Size of a set in mathematics
presented ten unsolved problems (of a total of 23, later published, now called Hilbert's problems). Of these, he placed "Cantor's problem" (now called the Continuum
Cardinality
Axiom in set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Axiom_of_global_choice
Informal set theories
be the realm of axiomatic set theory or of axiomatic class theory. The problem, in this context, with informally formulated set theories, not derived
Naive_set_theory
German-Israeli mathematician and Zionist (1891–1965)
האוניברסיטה העברית 1943c. "Problems and Methods in Modern Mathematics – 1". In Scripta Mathematica IX (1). 1943d. "Problems and Methods in Modern Mathematics
Abraham_Fraenkel
Axiom of set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Axiom_of_regularity
Paradox in set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Burali-Forti_paradox
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Paradoxes_of_set_theory
Concept in set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Axiom_schema_of_replacement
System of mathematical set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
General_set_theory
System of mathematical set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Kripke–Platek_set_theory
Possible axiom for set theory in mathematics
◊+ (and hence also Ostaszewski's club principle ♣) The negation of the Suslin hypothesis Global square The existence of morasses The non-existence of
Axiom_of_constructibility
Axiom in the mathematical field of set theory
are no Suslin lines). MA + ¬CH implies that there exists a Whitehead group that is not free; Shelah used this to show that the Whitehead problem is independent
Martin's_axiom
Template that specifies one or more axioms
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Axiom_schema
Theorem equivalent to the Axiom of Choice
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Tarski's_theorem_about_choice
Any collection of sets, or subsets of a set
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Family_of_sets
Principle in set theory
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Axiom_of_adjunction
Diophantine set Hyperarithmetical set Analytical set Analytic set, Coanalytic set Suslin set Projective set Inhabited set Multiset List of set identities and relations –
List_of_types_of_sets
Concept in mathematics
Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg
Axiom_of_countable_choice
Hungarian and American mathematician and physicist (1903–1957)
tool to brute force the solution to a problem numerically, but could also provide insight for solving problems analytically, and that there was an enormous
John_von_Neumann
SUSLINS PROBLEM
SUSLINS PROBLEM
Surname or Lastname
English
English : variant of Hoskins.
Surname or Lastname
English
English : variant of Pullen, with patronymic -s.
Surname or Lastname
English
English : perhaps a variant of Bullen or an altered form of Bullions, a variant of Bullion.
Girl/Female
Muslim/Islamic
Morning Star
Boy/Male
Arabic, Muslim
Slave of the One who Gives Life and Sustains it
Boy/Male
Indian
God of Shiva
Surname or Lastname
English (Essex)
English (Essex) : variant spelling of Sullens.
Boy/Male
Arabic, Muslim
One who Gives Life and Sustains it
Surname or Lastname
English and Irish
English and Irish : occupational name from Old French molineux ‘miller’ (see Molyneux).William Mullins (d. 1621) was one of the Pilgrims who sailed on the Mayflower in 1620. He, his wife, and his son died during the first winter at Plymouth Colony, leaving behind his daughter Priscilla, who married John Alden, by whom she had eleven children.
Surname or Lastname
English
English : variant of Mullins.
Boy/Male
Arabic, Muslim
Slave of the One who Gives Life and Sustains it
Boy/Male
Muslim/Islamic
Slave of the one who gives life and sustains it
Biblical
who nourishes, consumes, and sustains the whole
Surname or Lastname
English and Irish
English and Irish : variant of Mullins.
Girl/Female
Arabic, Muslim
Morning Star
Girl/Female
Arabic
Princess of the Muslims; Maker of Dresses
Surname or Lastname
English (Essex)
English (Essex) : variant of Sullen.
Boy/Male
Biblical
Who nourishes, consumes, and sustains the whole.
Boy/Male
Muslim
Slave of the one who gives life and sustains it
Girl/Female
Muslim
Morning star
SUSLINS PROBLEM
SUSLINS PROBLEM
Boy/Male
Muslim
Wealthy
Girl/Female
Muslim/Islamic
Near close
Female
Yiddish
(בֵּיילֶע) Yiddish form of Hebrew Bilhah, BAILE means "weak, troubled, old."
Boy/Male
American, British, English
Dark Skinned; Coal Miner
Boy/Male
Indian
Bright, Shining
Boy/Male
Tamil
Soul, Life force
Boy/Male
Gaelic
Pale.
Girl/Female
American, Australian, British, English
God is Gracious; From Jenny and Nell
Surname or Lastname
English
English : patronymic from Bay.
Girl/Female
Indian
Old ancient, Beautiful, Charitable, Loving
SUSLINS PROBLEM
SUSLINS PROBLEM
SUSLINS PROBLEM
SUSLINS PROBLEM
SUSLINS PROBLEM
n.
One who sustains a great burden.
pl.
of Sully
n.
A seaweed. See Baddrelocks.
a.
Belonging to sutlers; engaged in the occupation of a sutler.
n.
A thin cotton, white, dyed, or printed. The name is also applied to coarser and heavier cotton goods; as, shirting and sheeting muslins.
n.
The suslik.
a.
Trodden by buskins; pertaining to tragedy.
v. t.
To keep from falling; to bear; to uphold; to support; as, a foundation sustains the superstructure; a beast sustains a load; a rope sustains a weight.
n.
See Suslik.
n.
The suslik.
n.
One who, or that which, sustains.
n.
A kind of muslin.
a.
Wearing buskins.
n.
Coarse plain India muslins.
n.
Muslin.
n.
That which sullies or defiles.
n.
A sour, morose fellow.