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Sets Theory Assignment help

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Topics for Sets Theory

abstract mathematical thinking, basic definitions, relations, functions, equivalence relations, inductive sets, cardinality of sets, Logic, propositional calculus, first-order logic, semantics, proof systems, soundness, completeness theorems, compactness theorem, philosophical overtones, paradoxes, Russell, Cantor, Burali-Forti, motivating axiomatic, Zermelo-Fraenkel, axioms, axiom schemata, Transfinite induction, recursion, cardinal numbers, ordinal numbers, real number system , Zermelo-Fraenkel set theory, Continuum Hypothesis, Inaccessible Cardinals, 

The cumulative hierarchy
The axioms for Zermelo-Fraenkel's set theory
Ordered sets: partial and linear orderings
well-founded relations
The axiom of choice and equivalent variants
Zorn's lemma and the well-ordering principle
Transfinite induction and recursion.
Ordinals and cardinals
The continuum hypothesis
independence results and models of set theories
category theory


Set Theory & Mathematical Logic


the Zermelo-Fraenkel Axioms
Axiom of Choice
Transfinite arithmetic
Zorn's Lemma
Ordinal numbers
Cardinal numbers
model theory
Propositional & predicate calculus
soundness & completeness of formal languages
recursive functions & computability
Godel's incompleteness theorems

The axioms of set theory
The axioms of ZFC
The theory of transfinite ordinals and cardinals
The universe VV of all sets
Set theory as the foundation of mathematics
The incompleteness phenomenon
The set theory of the continuum
Descriptive Set Theory
The Continuum Hypothesis
Gödel's constructible universe
Other applications of forcing
The search for new axioms
Large cardinals
Inner models of large cardinals
Consequences of large cardinals
Forcing axioms





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