Question

If a set of sentences $\Delta$ is satisfiable and $\Delta \subseteq \Gamma$, then $\Gamma$ must also be satisfiable. Show that this does not hold.

score 250 · Answer 1 · 2020-04-23 09:03:29

250

Views

If a set of sentences $\Delta$ is satisfiable and $\Delta \subseteq \Gamma$, then $\Gamma$ must also be satisfiable. Show that this does not hold.

Published on 23 Apr 2020 - 9:03

score 228 · Answer 2 · 2026-03-29 04:48:18

228

Views

What does it mean for two theories to be inter-interpretable?

Published on 29 Mar 2026 - 4:48

score 405 · Answer 3 · 2020-04-24 16:35:14

405

Views

proving corollary of compactness theorem

Published on 24 Apr 2020 - 16:35

score 76 · Answer 4 · 2020-04-25 18:00:51

76

Views

Show that, if for every non-denumerable $\mathcal{M}$, $\mathcal{M} \not\models \Gamma$, then $\Gamma$ is unsatisfiable.

Published on 25 Apr 2020 - 18:00

score 447 · Answer 5 · 2020-04-26 04:21:57

447

Views

Theory vs complete diagram of a model

Published on 26 Apr 2020 - 4:21

score 354 · Answer 6 · 2020-04-26 11:01:25

354

Views

Verification for Proof of Compactness Theorem

Published on 26 Apr 2020 - 11:01

score 91 · Answer 7 · 2020-04-26 13:57:38

91

Views

What is the cardinality (finite, infinite and countable, or infinite and uncountable) of the smallest model of the following set?

Published on 26 Apr 2020 - 13:57

score 160 · Answer 8 · 2020-04-26 19:51:43

160

Views

Question on recusively saturated model

Published on 26 Apr 2020 - 19:51

score 186 · Answer 9 · 2026-03-28 08:17:15

186

Views

Model theory substitution notation

Published on 28 Mar 2026 - 8:17

score 64 · Answer 10 · 2020-04-27 15:08:16

64

Views

If a model $\mathcal{M}$ is s.t. $\mathcal{M} \models \Delta$ and $\mathcal{M} \models \Gamma$, then $\mathcal{M} \models \Delta \cup \Gamma$?

Published on 27 Apr 2020 - 15:08

score 304 · Answer 11 · 2020-04-27 19:06:12

304

Views

$ \models A$ vs. $ A \models$

Published on 27 Apr 2020 - 19:06

score 162 · Answer 12 · 2020-04-29 02:21:00

162

Views

If every finite subfamily of $\mathcal{F}$ has a transversal of size $n$, does $\mathcal{F}$ have the following intersection property?

Published on 29 Apr 2020 - 2:21

score 246 · Answer 13 · 2020-04-29 17:07:31

246

Views

Are $\Pi_2$ consequences of universal theories witnessed by finitely many terms?

Published on 29 Apr 2020 - 17:07

score 132 · Answer 14 · 2026-03-26 06:27:55

132

Views

Proving Unprovability: Is Compactness Used in the Metathory?

Published on 26 Mar 2026 - 6:27

score 146 · Answer 15 · 2026-03-28 16:44:41

146

Views

Does having many models yield complex second-order theories?

Published on 28 Mar 2026 - 16:44

List Question

If a set of sentences $\Delta$ is satisfiable and $\Delta \subseteq \Gamma$, then $\Gamma$ must also be satisfiable. Show that this does not hold.

What does it mean for two theories to be inter-interpretable?

proving corollary of compactness theorem

Show that, if for every non-denumerable $\mathcal{M}$, $\mathcal{M} \not\models \Gamma$, then $\Gamma$ is unsatisfiable.

Theory vs complete diagram of a model

Verification for Proof of Compactness Theorem

What is the cardinality (finite, infinite and countable, or infinite and uncountable) of the smallest model of the following set?

Question on recusively saturated model

Model theory substitution notation

If a model $\mathcal{M}$ is s.t. $\mathcal{M} \models \Delta$ and $\mathcal{M} \models \Gamma$, then $\mathcal{M} \models \Delta \cup \Gamma$?

$ \models A$ vs. $ A \models$

If every finite subfamily of $\mathcal{F}$ has a transversal of size $n$, does $\mathcal{F}$ have the following intersection property?

Are $\Pi_2$ consequences of universal theories witnessed by finitely many terms?

Proving Unprovability: Is Compactness Used in the Metathory?

Does having many models yield complex second-order theories?

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