Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 22nd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added the [Tarski reference](http://golem.ph.utexas.edu/category/2011/12/on_the_law_of_large_numbers_su.html#c040541) to [[intuitionistic logic]] and [[internal logic]]

   I have added the Tarski reference to intuitionistic logic and internal logic

2. • CommentRowNumber2.
   • CommentAuthorGuest
   • CommentTimeOct 14th 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexWhat is the "world's simplest axiom of choice"?

   What is the “world’s simplest axiom of choice”?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 18th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Arend Heyting]], *Die formalen Regeln der intuitionistischen Logik. I, II, III.* Sitzungsberichte der Preußischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse (1930) 42-56, 57-71, 158-169. I am not the first to ask the following, but it deserves asking again: Is there any electronic trace (scan, transcript) of this text? And: What's the next-best secondary source? (Review or textbook, from which the content of Heyting's text could be gleaned?) <a href="https://ncatlab.org/nlab/revision/diff/intuitionistic+logic/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/intuitionistic+logic/19">v19</a>, <a href="https://ncatlab.org/nlab/show/intuitionistic+logic">current</a>

   added pointer to:

   • Arend Heyting, Die formalen Regeln der intuitionistischen Logik. I, II, III. Sitzungsberichte der Preußischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse (1930) 42-56, 57-71, 158-169.

   I am not the first to ask the following, but it deserves asking again: Is there any electronic trace (scan, transcript) of this text?

   And: What’s the next-best secondary source? (Review or textbook, from which the content of Heyting’s text could be gleaned?)

   diff, v19, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 18th 2023
   • (edited Feb 18th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexStarted a section ([here](https://ncatlab.org/nlab/show/intuitionistic+logic#ConstructiveInterpretationOfConnectives)) for the "Constructive interpretation of the connectives", with a scan of the list of "interpretation of logical connectives" * [[Douglas Bridges]], p. 96 of: *Constructive mathematics: a foundation for computable analysis*, Theoretical Computer Science **219** 1–2 (1999) 95-109 &lbrack;<a href="https://doi.org/10.1016/S0304-3975(98)00285-0">doi:10.1016/S0304-3975(98)00285-0</a>&rbrack; In Bridges' text this is followed by a pointer to [Heyting (1930)](https://ncatlab.org/nlab/show/intuitionistic+logic#Heyting1930), though it remains ambiguous whether Bridges means to credit the list of rules (e.g. "to prove $A \vee B$ is to prove $A$ or to prove $B$" etc.) to Heyting, or "just" their further formalization. If not due to Heyting, I gather the list of these rules must have been formulated by Brouwer previously, or else maybe by Kolmogorov? What's a truly original reference? <a href="https://ncatlab.org/nlab/revision/diff/intuitionistic+logic/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/intuitionistic+logic/19">v19</a>, <a href="https://ncatlab.org/nlab/show/intuitionistic+logic">current</a>

   Started a section (here) for the “Constructive interpretation of the connectives”, with a scan of the list of “interpretation of logical connectives”

   • Douglas Bridges, p. 96 of: Constructive mathematics: a foundation for computable analysis, Theoretical Computer Science 219 1–2 (1999) 95-109 [doi:10.1016/S0304-3975(98)00285-0]

   In Bridges’ text this is followed by a pointer to Heyting (1930), though it remains ambiguous whether Bridges means to credit the list of rules (e.g. “to prove $A \vee B$ is to prove $A$ or to prove $B$” etc.) to Heyting, or “just” their further formalization.

   If not due to Heyting, I gather the list of these rules must have been formulated by Brouwer previously, or else maybe by Kolmogorov? What’s a truly original reference?

   diff, v19, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeFeb 18th 2023
   • (edited Feb 18th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexthanks to a private email, I see that an abridged reprint of Heyting (1930) is in: * Karel Berka, Lothar Kreiser (eds.), *Logik-Texte*, De Gruyter (1986) 188-192 &lbrack;[doi:10.1515/9783112645826](https://doi.org/10.1515/9783112645826)&rbrack; Have added the pointer here. <a href="https://ncatlab.org/nlab/revision/diff/intuitionistic+logic/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/intuitionistic+logic/20">v20</a>, <a href="https://ncatlab.org/nlab/show/intuitionistic+logic">current</a>

   thanks to a private email, I see that an abridged reprint of Heyting (1930) is in:

   • Karel Berka, Lothar Kreiser (eds.), Logik-Texte, De Gruyter (1986) 188-192 [doi:10.1515/9783112645826]

   Have added the pointer here.

   diff, v20, current