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15
58
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Model theoretic translation of Hilbert's Basis Theorem

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#logic #commutative-algebra #model-theory
124
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Proof that a set of axioms axiomatizes the complex field along with the real numbers

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#model-theory
158
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Can a subgroup of the symmetric group $\mathfrak S_k$ be an elementary substructure?

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#group-theory #logic #predicate-logic #model-theory #symmetric-groups
408
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Theory of infinite vector spaces admits quantifier elimination

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#logic #first-order-logic #model-theory #quantifier-elimination
240
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Clarify on Birkhoff's theorem (in universal algebra)

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#abstract-algebra #logic #model-theory #universal-algebra
63
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Viewing $L_M$-formulas as $L$-formulas, and restriction of $L_M$-structures

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#logic #model-theory
99
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Compactness theorem equivalences

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#logic #compactness #first-order-logic #model-theory
335
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What is an example of model of ZF with a countable family of pairs whose union is uncountable?

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#set-theory #model-theory #axiom-of-choice
90
Views

Clarify on a strong form of the compactness theorem (in first order logic)

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#first-order-logic #model-theory
150
Views

Show that $C = C_A = \{\sigma < \omega_1 : M_{A,\sigma} \cap \omega_1 = \sigma\}$ is a club

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#logic #set-theory #model-theory #infinitary-combinatorics
517
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What theories are preserved under the product?

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#logic #model-theory #universal-algebra #direct-product
320
Views

Can metalogic and model theory be formalized?

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#logic #model-theory #foundations #meta-math #metalogic
159
Views

Prove: Impossible to express "There are at least 7 objects" by quantifying over only 6 variables

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#logic #first-order-logic #model-theory #natural-numbers
76
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Decidability of fragments of many-sorted first-order logic

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#logic #reference-request #model-theory #decidability
111
Views

How to model structures over a proper class?

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#logic #set-theory #first-order-logic #model-theory #foundations

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