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Free objects as term algebras in universal algebra and free modules

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#abstract-algebra #logic #vector-spaces #model-theory #universal-algebra
187
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Ehrenfeucht-Fraisse games over finite sequences (i.e. words) and separability by first order formulas

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#logic #first-order-logic #model-theory #game-theory #formal-languages
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Some $\Pi^1_1$ sentences are elementary

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#logic #model-theory
64
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Clubs and some fixed type is realized by uncountably many elements.

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#logic #model-theory #ordinals
2.4k
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Is there a *simple* example of how the axiom of choice can lead to a counterintuitive result?

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#logic #model-theory #axiom-of-choice
58
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What does $C,D \models \delta$ mean?

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#logic #first-order-logic #model-theory
72
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Is the formula $\exists x : x^2-a=0$ not downward absolute over the theory of field of rational numbers?

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#logic #model-theory
174
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an example of a formula which divides in the theory of algebraically closed fields

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#logic #model-theory
68
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First order formula that is true in a structure with $f(x)=x^2$ but not in a structure with $f(x)=x^3$

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#logic #predicate-logic #model-theory
188
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How to construct a model to satisfy first order logic sentences

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#logic #first-order-logic #predicate-logic #model-theory
889
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Is it possible to express the following in First Order logic?

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#logic #first-order-logic #predicate-logic #model-theory
118
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Systems of arithmetic models

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#logic #first-order-logic #model-theory #peano-axioms #presburger-arithmetic
100
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A set of sentences true under an arbitrarily large finite models, then it is true under some infinite model

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#logic #model-theory
85
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Putting a total ordering into set theory compatible with the Ackermann interpretation on $V_\omega$.

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#proof-verification #set-theory #model-theory
353
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A quotient of a product of prime characteristic fields is isomorphic to a subfield of $\mathbf{C}$

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#abstract-algebra #field-theory #finite-fields #model-theory #filters

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