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Why does an M-Ultrafilter on $\kappa$ imply that $\kappa$ is weakly compact?

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#set-theory #large-cardinals
112
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Proving the categoricity of an extension of ZFC2

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#proof-writing #set-theory #large-cardinals
129
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Classify this Large Cardinal

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#set-theory #large-cardinals
147
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What axiomatic set theories say that large cardinals exist

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#set-theory #large-cardinals
134
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Equi-consistency of inaccessible cardinals

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#set-theory #large-cardinals
202
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Equivalence of the existence of some ultrafilter and some elementary embedding

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#set-theory #large-cardinals
205
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Ramsey property and linear orders on $\kappa$

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#set-theory #ramsey-theory #large-cardinals
212
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Large Cardinals and Diophantine Equations (Penelope Maddy)

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#logic #set-theory #diophantine-equations #large-cardinals #decidability
100
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Mahlo operation, consistency border

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#set-theory #cardinals #large-cardinals
149
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2-huge cardinal, the most usual definition

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#set-theory #cardinals #large-cardinals
106
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Ultrapower of V by D

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#set-theory #large-cardinals
269
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Huge vs. compact cardinal

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#set-theory #large-cardinals
70
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Group theoretic Characterizations of Large Cardinals

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#group-theory #big-list #large-cardinals
205
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Can there be a proper class of $\alpha$-inaccessibles for any ordinal $\alpha$?

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#set-theory #large-cardinals
124
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Does exist a singular cardinal $\lambda$ which $\kappa < \lambda \implies 2^{\kappa}<\lambda?$

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#set-theory #large-cardinals

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