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150
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Can $ZFC + \neg Con(ZFC)$ be interpretable in $PA + \omega$- rule?

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#set-theory #first-order-logic
80
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Is "PA+ω-rule" and "Zermelo-infinity+every set is finite + ω-set-rule" equi-interpretable?

Published on
#logic #set-theory #first-order-logic
158
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Baire space $\mathbb{N}^\mathbb{N}$ written as $\mathbb{R}$

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#set-theory #real-numbers #descriptive-set-theory #the-baire-space
91
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Show that there exists non-zero countable ordinal $\delta$ such that $\omega\delta=\delta$

Published on
#set-theory #ordinals
174
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Uses of Axiom of Choice

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#set-theory
80
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Which stage in the Neumann hierarchy do powers of the reals fit in?

Published on
#functional-analysis #set-theory #exponentiation #real-numbers #cardinals
171
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What is the lowest layer of the Constructible Universe which is a model of $ZFC-P$?

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#logic #set-theory #model-theory #ordinals #ordinal-analysis
87
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Given a poset with a join such that any pair has a meet, find a total order with a special property.

Published on
#set-theory #order-theory #ordinals #well-orders
139
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Finding an order isomorphism from $\text{On}\times\text{On}$ to $\text{On}$

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#set-theory #order-theory #ordinals
203
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Cantor-Bendixson Theorem Proof (existence of an ordinal)

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#general-topology #set-theory #ordinals #descriptive-set-theory
113
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Is there a subsystem of ZFC which constrains the Universe to $L$?

Published on
#logic #set-theory #axiom-of-choice #ordinals #constructive-mathematics
161
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Can we describe any subsets of $\mathbb{N}$ occurring in a late layer of the Constructible Universe?

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#logic #set-theory #computability #ordinals #descriptive-set-theory
66
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How to compare values of Buchholz functions?

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#set-theory #ordinals
56
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Prove that $A=\{\{\Phi(b\restriction n) : n \in\omega\}\mid b\colon\omega\to 2\}$ is not a mad family.

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#set-theory
75
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Is $\forall x(x\in L\land\mathrm{rank}(x)=\alpha\rightarrow x\in L_{\alpha+1})$ consistent with $\mathsf{ZFC}$?

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#set-theory

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