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Hyperfinite intervals are uncountable but nonstandard models of Peano arithmetic can be countable?

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#model-theory #nonstandard-analysis #nonstandard-models
49
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measurability for function on internal measure space

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#measure-theory #nonstandard-analysis #nonstandard-models
108
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Question about the definition of superstructure

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#model-theory #nonstandard-analysis #nonstandard-models
159
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Do the properties of the hyperreal numbers change depending on the ultrafilter used?

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#logic #set-theory #nonstandard-analysis #nonstandard-models
82
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Any set can be easily replaced by a base set with the same size

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#model-theory #nonstandard-analysis #nonstandard-models
132
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Is There a notion of Convergence for the Non-Standard Reals? How can we do Analysis?

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#soft-question #nonstandard-analysis #nonstandard-models
40
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Uniformly Bounded Functions of Hyperreals

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#uniform-convergence #nonstandard-analysis #infinitesimals #nonstandard-models
139
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Strongest tools to detect unsoundness

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#logic #proof-theory #foundations #provability #nonstandard-models
118
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Why Quantifier Free Formulas define Linear Functions.

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#model-theory #peano-axioms #quantifier-elimination #nonstandard-models
250
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Are There Numbers Beyond the Reals?

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#elementary-set-theory #real-numbers #nonstandard-models
458
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Why aren't there any first-order sentences which have the property of being true in all non-standard models of PA and false in the standard one?

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#first-order-logic #higher-order-logic #nonstandard-models
130
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Nonstandard models of PA with a decidable order relation.

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#logic #model-theory #computability #nonstandard-models
363
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The order-theoretic structure of the ordinal numbers in non-standard models

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#logic #set-theory #ordinals #nonstandard-models
125
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One-element model of first-order PA

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#number-theory #model-theory #natural-numbers #peano-axioms #nonstandard-models
379
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Gödel's way of teaching non-standard models to Takeuti.

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#logic #model-theory #proof-theory #incompleteness #nonstandard-models

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