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Books/Resources for studying Number Theory as a First Order Theory and Model Theory

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#logic #soft-question #first-order-logic #model-theory
459
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What formula of ZFC defines the set of natural numbers?

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#logic #model-theory #foundations #natural-numbers
123
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Is there a class of finite graphs that can be axiomatized by existential second-order formulas but it's complement couldn't? (edited)

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#logic #graph-theory #model-theory #second-order-logic
388
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Exercise 2.5.5 david marker's

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#logic #first-order-logic #model-theory
95
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A model satisfying the existence of a model

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#set-theory #model-theory
243
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Proving Compactness Theorem

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#logic #first-order-logic #model-theory
52
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What does it mean, terminology-wise, for a set of formulas to be positive in Q?

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#model-theory
154
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Reference request - Model theory

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#logic #reference-request #model-theory
104
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Model theory preliminaries

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#logic #first-order-logic #model-theory
231
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Existence of direct limit in model theory

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#logic #proof-explanation #set-theory #model-theory
137
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Proof of the equivalence of validity of formula and its closure in a structure (Shoenfield's book)

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#logic #first-order-logic #model-theory
311
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Non-rigid ultrapowers in $\mathsf{ZFC}$

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#logic #set-theory #model-theory #filters
208
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applying Martin's axiom

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#logic #set-theory #model-theory #descriptive-set-theory #forcing
80
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Can natural numbers with multiplication alone define the order relation?

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#model-theory
48
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If the set of S-formula in FOL is infinite, then what means a model can interpret this set?

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#logic #model-theory

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