Question

During model constructions we always have cardinality restrictions on the models (ex: $|M| \leq |L| + \aleph_0$ or $|M| \geq |L| + \aleph_0$). Why?

score 68 · Answer 1 · 2020-09-25 20:35:12

During model constructions we always have cardinality restrictions on the models (ex: $|M| \leq |L| + \aleph_0$ or $|M| \geq |L| + \aleph_0$). Why?

score 123 · Answer 2 · 2026-04-12 21:07:01

123

Views

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score 76 · Answer 3 · 2026-04-12 23:58:58

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score 76 · Answer 4 · 2026-04-13 18:02:52

76

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244

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score 56 · Answer 7 · 2020-10-01 02:25:27

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score 138 · Answer 8 · 2020-10-01 18:59:15

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Model of cardinality $\lambda$ where every definable subset is either finite or has size $\lambda$

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score 556 · Answer 9 · 2026-04-11 04:41:19

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score 63 · Answer 10 · 2020-10-04 12:30:06

63

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score 69 · Answer 11 · 2026-04-11 20:28:14

69

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score 53 · Answer 12 · 2020-10-05 08:34:35

53

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score 88 · Answer 13 · 2026-04-12 20:26:53

88

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score 115 · Answer 14 · 2026-04-13 01:57:46

115

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score 753 · Answer 15 · 2026-03-25 13:53:36

753

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List Question

During model constructions we always have cardinality restrictions on the models (ex: $|M| \leq |L| + \aleph_0$ or $|M| \geq |L| + \aleph_0$). Why?

Pigeonhole principle and the random graph

Given a transitive model $M$, is it possible to have both $X \in M$ and $X^M \not = X$?

Does it make sense to talk about absoluteness of concepts, or just formulas? (Soft question)

Confusion regarding what a valid sentence is in model theory

Isomorphic elementary substructure with equal predicates, and stronger(?) lowenheim skolem

The finite partition of a random graph has an element that is a random graph

Model of cardinality $\lambda$ where every definable subset is either finite or has size $\lambda$

Subgroups defined by negative formulas

Show that negation is a definable function in $\langle \mathbb{R}, +, 0 \rangle$

Applying compactness theorem to show a property of a theory $K$

There is only a finite number of interpretations of a wf $\mathcal{B}$ on a domain with cardinality $k$

Why are the Peano axioms axioms for natural numbers if they have non-standard models?

Absoluteness of constructibility of sets

How can induction work on non-standard natural numbers?

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