Question

Why do we know that Gödel sentences are true in the standard model of set theory, but do not know if the continuum hypothesis is?

score 1.3k · Answer 1 · 2015-06-30 21:36:00

1.3k

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Why do we know that Gödel sentences are true in the standard model of set theory, but do not know if the continuum hypothesis is?

Published on 30 Jun 2015 - 21:36

score 326 · Answer 2 · 2026-03-25 06:05:46

326

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Non-standard model of $Th(\mathbb{R})$ with the same cardinality of $\mathbb{R}$

Published on 25 Mar 2026 - 6:05

score 244 · Answer 3 · 2015-07-04 14:43:17

244

Views

Number of non-isomorphic models

Published on 04 Jul 2015 - 14:43

score 111 · Answer 4 · 2015-07-04 15:00:10

111

Views

$\kappa$-categoricity in the language of identity

Published on 04 Jul 2015 - 15:00

score 481 · Answer 5 · 2015-07-04 20:23:14

481

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Ultraproducts explicit example

Published on 04 Jul 2015 - 20:23

score 61 · Answer 6 · 2015-07-06 20:12:07

61

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Questions concerning a specific given theory.

Published on 06 Jul 2015 - 20:12

score 1.3k · Answer 7 · 2015-07-08 09:32:42

A substructure that is elementary equivalent to its structure, isn't an elementary substructure example mistake?

score 57 · Answer 8 · 2015-07-08 19:59:23

For signature $s= \{ f\}, n_f=1$, show that if for structures $M, N$, $f^N, f^M$ have only one orbit, of infinite order, then $M,N$ are isomorphic

score 223 · Answer 9 · 2015-07-09 07:11:50

223

Views

Application of the reflection theorem in ZFC

Published on 09 Jul 2015 - 7:11

score 93 · Answer 10 · 2015-07-10 10:31:14

93

Views

Let $T$ be a theory over $S$, prove that $T \vdash \{\phi \rightarrow \psi \} \iff (T \cup \phi) \vdash \psi$

Published on 10 Jul 2015 - 10:31

score 360 · Answer 11 · 2015-07-10 20:31:23

Proving that for structure $M=(\mathbb R; +,<,0)$, the function $f(x,y)=x \cdot y$ is not a definable set in $M$

score 50 · Answer 12 · 2015-07-11 10:31:45

50

Views

Over signature $S= \{f \}$, $n_f=1$, find a formula $\phi$ so that for every structure, $M \vDash \phi \implies|M|$ is infinite

Published on 11 Jul 2015 - 10:31

score 3.7k · Answer 13 · 2015-07-11 23:25:20

3.7k

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Elementary substructure and elementary equivalence

Published on 11 Jul 2015 - 23:25

score 416 · Answer 14 · 2026-03-25 06:09:18

416

Views

Quantifier elimination over rationals.

Published on 25 Mar 2026 - 6:09

score 157 · Answer 15 · 2015-07-13 18:45:39

Model theory exam question:Show that if $M$ is isomorphic to $N$, then there is an extention to signature $S*$ so that $M*$ isomorphic to $N*$

List Question

Why do we know that Gödel sentences are true in the standard model of set theory, but do not know if the continuum hypothesis is?

Non-standard model of $Th(\mathbb{R})$ with the same cardinality of $\mathbb{R}$

Number of non-isomorphic models

$\kappa$-categoricity in the language of identity

Ultraproducts explicit example

Questions concerning a specific given theory.

A substructure that is elementary equivalent to its structure, isn't an elementary substructure example mistake?

For signature $s= \{ f\}, n_f=1$, show that if for structures $M, N$, $f^N, f^M$ have only one orbit, of infinite order, then $M,N$ are isomorphic

Application of the reflection theorem in ZFC

Let $T$ be a theory over $S$, prove that $T \vdash \{\phi \rightarrow \psi \} \iff (T \cup \phi) \vdash \psi$

Proving that for structure $M=(\mathbb R; +,<,0)$, the function $f(x,y)=x \cdot y$ is not a definable set in $M$

Over signature $S= \{f \}$, $n_f=1$, find a formula $\phi$ so that for every structure, $M \vDash \phi \implies|M|$ is infinite

Elementary substructure and elementary equivalence

Quantifier elimination over rationals.

Model theory exam question:Show that if $M$ is isomorphic to $N$, then there is an extention to signature $S$ so that $M$ isomorphic to $N*$

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