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Considering a non-standard set theory

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Can one-element set be considered equal to its element?

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Positive set theory, antifoundation, and the "co-Russell set"

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#logic #set-theory #foundations #alternative-set-theories
154
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Cardinality of the set of truth values in a Heyting-valued model of IZF

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#constructive-mathematics #intuitionistic-logic #alternative-set-theories
66
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Are there set theories making the class-as-many and class-as-one distinction?

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Is there a contradiction hiding in this alternative set theory with 3 axioms?

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#logic #foundations #alternative-set-theories
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Why use ZF over NFU?

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#set-theory #alternative-set-theories
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Alternative set theories

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#soft-question #set-theory #education #alternative-set-theories
76
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Is there an obvious inconsistency with this set theory?

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#first-order-logic #alternative-set-theories
98
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Unique Existence In Local Set Theories

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#logic #category-theory #model-theory #topos-theory #alternative-set-theories
190
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Substitution In Logic

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#logic #category-theory #topos-theory #alternative-set-theories
85
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Elementary Embeddings of Transitive Models of ZFA

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#set-theory #alternative-set-theories
97
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Does $X^A = Y^B \Longrightarrow X=Y \wedge A=B$? (ETCS)

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#category-theory #alternative-set-theories
68
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Is there any successful approach to algebraization of set theory other than the category-theoretical approach?

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138
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Set Theory without Powerset

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