User Apostolos

26 votes

Accepted

Do sets, whose power sets have the same cardinality, have the same cardinality?

answered Mar 27, 2011 at 21:47

16 votes

Accepted

Prove 7 divides $15^n+6$ with mathematical induction

answered Feb 16, 2011 at 12:10

15 votes

Accepted

Prove that $\beta \rightarrow \neg \neg \beta$ is a theorem using standard axioms 1,2,3 and MP

answered Oct 1, 2010 at 12:08

14 votes

Accepted

Naive set theory question on "="

answered Mar 2, 2011 at 2:01

13 votes

Accepted

Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$

answered Feb 23, 2013 at 12:53

12 votes

Accepted

An Exercise in Kunen (A Model for Foundation, Pairing,...)

answered Jun 27, 2013 at 12:17

11 votes

Accepted

Cardinality of the infinite sets

answered Jun 6, 2011 at 21:58

11 votes

Accepted

Conditions Equivalent to Injectivity

answered Nov 5, 2011 at 19:52

11 votes

Cofinality and its Consequences

answered Mar 4, 2011 at 12:47

10 votes

Accepted

Proof: Cartesian Product of Two Sets is a Set ZF

answered Mar 12, 2011 at 13:06

9 votes

Accepted

Logic, set theory, independence proofs, etc

answered Mar 21, 2011 at 0:07

9 votes

Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?

answered Apr 1, 2011 at 12:37

9 votes

How do the separation axioms follow from the replacement axioms?

answered Apr 12, 2011 at 6:46

9 votes

How to prove that from "Every infinite cardinal satisfies $a^2=a$" we can prove that $b+c=bc$ for any two infinite cardinals $b,c$?

answered Jul 1, 2011 at 8:16

9 votes

Metalogic: Prove $\{\neg P_1 \to P_2\} \vdash (\neg P_2\to P_1)$ without using the Deduction Theorem

answered Apr 28, 2011 at 7:43

9 votes

Accepted

Example of a not recursively enumerable set $A \subseteq \mathbb{N}$

answered May 9, 2011 at 7:30

9 votes

Does $\mathsf{ZFC} + \neg\mathrm{Con}(\mathsf{ZFC})$ suffice as a foundations of mathematics?

answered Apr 23, 2013 at 13:29

7 votes

Accepted

How to remove constant symbols from a first-order theory?

answered May 2, 2017 at 14:08

7 votes

Why is cofinality important? And some help in proving absoluteness for $R(\kappa)$

answered May 12, 2011 at 16:08

7 votes

Accepted

Does a "backwards" choice function imply the Axiom of Choice?

answered May 8, 2011 at 12:41

7 votes

Accepted

Tarski-Vaught test for $\preceq$ reduction

answered Jan 28, 2013 at 19:34

7 votes

Accepted

Question about the order of a Stationary subset of $ \kappa$

answered Jan 21, 2013 at 13:27

7 votes

Accepted

proof that union of a sequence of countable sets is countable.

answered Dec 14, 2011 at 7:32

7 votes

Is Robinson Arithmetic complete and not-complete?

answered Dec 4, 2010 at 15:58

7 votes

Accepted

On the definition of weakly compact cardinals

answered Sep 7, 2010 at 14:48

6 votes

Finitely axiomatizable theories

answered Dec 4, 2010 at 23:24

6 votes

Accepted

With Choice, is any linearly ordered set well-ordered if no subset has order type $\omega^*$?

answered Apr 9, 2011 at 22:02

6 votes

Measurable cardinal existence condition

answered Apr 20, 2012 at 7:22

6 votes

Non-isomorphic atomless Boolean algebras

answered May 22, 2012 at 19:25

6 votes

Accepted

Show that an elementary equivalent structure of $\mathbb{R}$ and definable from points is Dedekind complete

answered Jan 25, 2013 at 15:35

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95 Answers

Do sets, whose power sets have the same cardinality, have the same cardinality?

Prove 7 divides $15^n+6$ with mathematical induction

Prove that $\beta \rightarrow \neg \neg \beta$ is a theorem using standard axioms 1,2,3 and MP

Naive set theory question on "="

Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$

An Exercise in Kunen (A Model for Foundation, Pairing,...)

Cardinality of the infinite sets

Conditions Equivalent to Injectivity

Cofinality and its Consequences

Proof: Cartesian Product of Two Sets is a Set ZF

Logic, set theory, independence proofs, etc

Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?

How do the separation axioms follow from the replacement axioms?

How to prove that from "Every infinite cardinal satisfies $a^2=a$" we can prove that $b+c=bc$ for any two infinite cardinals $b,c$?

Metalogic: Prove $\{\neg P_1 \to P_2\} \vdash (\neg P_2\to P_1)$ without using the Deduction Theorem

Example of a not recursively enumerable set $A \subseteq \mathbb{N}$

Does $\mathsf{ZFC} + \neg\mathrm{Con}(\mathsf{ZFC})$ suffice as a foundations of mathematics?

How to remove constant symbols from a first-order theory?

Why is cofinality important? And some help in proving absoluteness for $R(\kappa)$

Does a "backwards" choice function imply the Axiom of Choice?

Tarski-Vaught test for $\preceq$ reduction

Question about the order of a Stationary subset of $ \kappa$

proof that union of a sequence of countable sets is countable.

Is Robinson Arithmetic complete and not-complete?

On the definition of weakly compact cardinals

Finitely axiomatizable theories

With Choice, is any linearly ordered set well-ordered if no subset has order type $\omega^*$?

Measurable cardinal existence condition

Non-isomorphic atomless Boolean algebras

Show that an elementary equivalent structure of $\mathbb{R}$ and definable from points is Dedekind complete