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- Discussion Type
- discussion topicUrysohn metrization theorem
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by Todd_Trimble
- Last Active 7 days ago

Created a stub for Urysohn metrization theorem.

- Discussion Type
- discussion topicMatériaux pour l'histoire des mathématiques au XXe siècle
- Category Latest Changes
- Started by Richard Williamson
- Comments 1
- Last comment by Richard Williamson
- Last Active 7 days ago

- Discussion Type
- discussion topicEsquisse d'un programme
- Category Latest Changes
- Started by Richard Williamson
- Comments 1
- Last comment by Richard Williamson
- Last Active 7 days ago

- Discussion Type
- discussion topicwell-founded relation
- Category Latest Changes
- Started by Todd_Trimble
- Comments 52
- Last comment by Todd_Trimble
- Last Active Aug 10th 2018

I added a proposition to this subsection which seems valid intuitionistically, but I wouldn’t mind a reality check from someone.

- Discussion Type
- discussion topicwell-ordering theorem
- Category Latest Changes
- Started by Todd_Trimble
- Comments 6
- Last comment by Richard Williamson
- Last Active Aug 10th 2018

Indicated where to find (in the nLab) a proof of the equivalence with the axiom of choice and with Zorn’s lemma (<– it’s there).

- Discussion Type
- discussion topicaxiom UIP
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Richard Williamson
- Last Active Aug 10th 2018

also created

*axiom UIP*, just for completeness. But the entry still needs some reference or else some further details.

- Discussion Type
- discussion topicHartogs number
- Category Latest Changes
- Started by Todd_Trimble
- Comments 21
- Last comment by Todd_Trimble
- Last Active Aug 9th 2018

Added a bit to Hartogs number. Including the curiosity that GCH implies AC. :-)

- Discussion Type
- discussion topiccardinal arithmetic
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Todd_Trimble
- Last Active Aug 9th 2018

- Discussion Type
- discussion topicExtrinsic/intrinsic Curry/Church distinctions
- Category Latest Changes
- Started by David_Corfield
- Comments 16
- Last comment by Mike Shulman
- Last Active Aug 8th 2018

We don’t have anything on this, I think, but there is mention of “intrinsic” and “à la Church” at coercion. From Type refinement and monoidal closed bifibrations:

One of the difficulties in giving a clear mathematical definition of the “topic” of type theory is that the word “type” is actually used with two very different intuitive meanings and technical purposes in mind:

- Like the syntactician’s parts of speech, as a way of defining the grammar of well-formed expressions.
- Like the semanticist’s predicates, as a way of identifying subsets of expressions with certain desirable properties.

These two different views of types are often associated respectively with Alonzo Church and Haskell Curry (hence “types à la Church” and “types à la Curry”), while the late John Reynolds referred to these as the intrinsic and the extrinsic interpretations of types [11]. In the intrinsic view, all expressions carry a type, and there is no need (or even sense) to consider the meaning of “untyped” expressions; while in the extrinsic view, every expression carries an independent meaning, and typing judgments serve to assert some property of that meaning.

[11] is John C. Reynolds. The Meaning of Types: from Intrinsic to Extrinsic Semantics. BRICS Report RS-00-32, Aarhus University, December 2000. pdf

There are two very different ways of giving denotational semantics to a programming language (or other formal language) with a nontrivial type system. In an intrinsic semantics, only phrases that satisfy typing judgements have meanings. Indeed, meanings are assigned to the typing judgements, rather than to the phrases themselves, so that a phrase that satisfies several judgements will have several meanings.

In contrast, in an extrinsic semantics, the meaning of each phrase is the same as it would be in a untyped language, regardless of its typing properties. In this view, a typing judgement is an assertion that the meaning of a phrase possesses some property.

The terms “intrinsic” and “extrinsic” are recent coinages by the author [1, Chapter 15], but the concepts are much older. The intrinsic view is associated with Alonzo Church, and has been called “ontological” by Leivant [2]. The extrinsic view is associated with Haskell Curry, and has been called “semantical” by Leivant.

[1] John C. Reynolds. Theories of Programming Languages. Cambridge University Press, Cambridge, England, 1998. [2] Daniel Leivant. Typing and computational properties of lambda expressions. Theoretical Computer Science, 44(1):51–68, 1986.

Anyone have a preferred name for this distinction?

- Discussion Type
- discussion topiclexicographic order
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by Todd_Trimble
- Last Active Aug 8th 2018

Created lexicographic order.

- Discussion Type
- discussion topicWalker-Wang model
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by David_Corfield
- Last Active Aug 8th 2018

created stub entry for

*Walker-Wang model*

- Discussion Type
- discussion topictopological insulator
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Aug 8th 2018

- Discussion Type
- discussion topicinfinite cardinal
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 7th 2018

- Discussion Type
- discussion topic12-dimensional supergravity
- Category Latest Changes
- Started by David_Corfield
- Comments 10
- Last comment by David_Corfield
- Last Active Aug 6th 2018

Started 12-dimensional supergravity following some discussion with Urs.

- Discussion Type
- discussion topicidentity type
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Mike Shulman
- Last Active Aug 5th 2018

added to identity type a mentioning of the alternative definition in terms of inductive types (paths).

- Discussion Type
- discussion topicHitoshi Nishino
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 5th 2018

brief category:people entry for hyperlinking references at

*12-dimensional supergravity*

- Discussion Type
- discussion topicGeorge Boole
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Aug 5th 2018

- Discussion Type
- discussion topicJames construction
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 5th 2018

gave this material, taken from the Examples-section at

*filtered topological space*, its own entryDidn’t touch the material beyond some trivial formatting and adding more references.

- Discussion Type
- discussion topicFiltered topological space
- Category Latest Changes
- Started by Colin Tan
- Comments 6
- Last comment by Urs
- Last Active Aug 5th 2018

Started to write up a homotopy-theoretic version of James construction following ideas of Brunerie’s IAS talk at filtered topological space

- Discussion Type
- discussion topicMiles Blencowe
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Aug 5th 2018

- Discussion Type
- discussion topicAdS-CFT in condensed matter physics
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 5th 2018

- Discussion Type
- discussion topicsupergravity
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by David_Corfield
- Last Active Aug 5th 2018

created supergravity

so far just an "Idea" section and a link to D'Auria-Fre formulation of supergravity (which i am busy working on)

- Discussion Type
- discussion topicmetabelian group
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Aug 4th 2018

- Discussion Type
- discussion topicnormal space
- Category Latest Changes
- Started by Todd_Trimble
- Comments 5
- Last comment by Richard Williamson
- Last Active Aug 4th 2018

- Discussion Type
- discussion topicnorm residue isomorphism theorem
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Aug 3rd 2018

- Discussion Type
- discussion topicMilnor's conjecture
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Aug 3rd 2018

- Discussion Type
- discussion topicHilbert cube
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Aug 3rd 2018

- Discussion Type
- discussion topicasymptotic boundary
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 3rd 2018

- Discussion Type
- discussion topicRandall-Sundrum model
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 3rd 2018

- Discussion Type
- discussion topicSteven Giddings
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 3rd 2018

brief category:people entry for hyperlinking references at

*super Riemann surface*and*Randall-sundrum model*