December 15, 2010

A Global Glance on Categories in Logic

Posted by John Baez

In a mocking, ironic nod to the concept of “open access”, Springer Verlag has made all papers in their journal Logica Universalis freely accessible from today until December 31st, 2010.

So, snatch as many papers you can before the great iron gate crashes closed again!

For example, if you’re curious about the interactions between logic and category theory, now is your chance to read this:

Many readers here will nod knowingly at the last sentence of this paper, which justifies some generalizations the authors have engaged in:

Second, on a more abstract level, it is a highly successful mathematical practice to admit pathological objects in a category in order to make (the global properties of) the category itself less pathological — the passage from manifolds to $C^\infty$-schemes in Differential Geometry illustrates well this point, as does the functorial approach to algebraic geometry, where one passes by the Yoneda embedding from schemes into a category of functors where most objects have no geometric appeal at all.

But be careful. Don’t be caught downloading papers from the Springer website when the clock strikes midnight on New Year’s Eve. There’s no telling what might happen.

Posted at December 15, 2010 2:04 AM UTC

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Re: A Global Glance on Categories in Logic

All the down-loadable articles there are named fulltext.pdf. Rather than manually renaming the PDFs or manually naming sub-directories to store them, this seems like a good application for Zotero. However, the Zotero parser for Springerlink is currently broken, and seems to have been broken since at least Sep. 23. You can still sort-of use Zotero keeping in mind that it won’t
1. extract bibliographic info, citations, etc. In fact it becomes rather hard to distinguish what it downloads so I resorted to making sub-folders like LogicaUniversalis/V3N1 etc.
2. won’t automatically download the PDFs (as it should if your options are set correctly). You can manually do this by saving an entry for each article page (click ICON = blue sheet of paper with green “+” at bottom) and then dragging the PDF link on top of the new entry.
The reason I’m mentioning this is that when Zotero gets its Springerlink scraper working again it may be possible to revisit these pages and get the bib info to update. Are there any articles particularly worth reading, rather than vacuuming up everything that might have potential for later perusal?
Posted by: Rod McGuire on December 15, 2010 8:22 PM | Permalink | Reply to this

Re: A Global Glance on Categories in Logic

I wasn’t actually advocating that people download all the Springer articles. I was just making a joke to express my amusement at the concept of ‘temporary open-access’.

Which papers are especially worth reading depends a lot on what kinds of logic you like. The folks at Springer sent me a list of their favorites, but it doesn’t seem to correspond to what I like, except for the article I mentioned in my post. Here’s their list.

Carnap, Goguen, and the Hyperontologies: Logical Pluralism and Heterogeneous Structuring in Ontology Design

Oliver Kutz, Till Mossakowski and Dominik Lücke

Information Algebras and Consequence Operators

Jürg Kohlas and Robert F. Stärk

On the 3D Visualisation of Logical Relations

Hans Smessaert

The Place of Logic in Reasoning

Daniel Kayser

A New Modal Lindstrom Theorem

Johan van Benthem

Birkhoff Completeness in Institutions

Mihai Codescu and Daniel Gaina

Symmetric Generalized Galois Logics

Katalin Bimbo and J. Michael Dunn

Strong Normalizability of Typed Lambda-Calculi for Substructural Logics

Motohiko Mouri and Norihiro Kamide

Some General Results About Proof Normalization

Marc Aiguier and Delphine Longuet

Many-Place Sequent Calculi for Finitely-Valued Logics

Alexej P. Pynko

Generalized Definitional Reflection and the Inversion Principle

Peter Schroeder-Heister

Structuralist Logic: Implications, Inferences, and Consequences

Arnold Koslow

A Global Glance on Categories in Logic

Peter Arndt, Rodrigo de Alvarenga Freire, Odilon Otavio Luciano and Hugo Luiz Mariano

Abstract Logics, Logic Maps, and Logic Homomorphisms

Steffen Lewitzka

From Fibring to Cryptofibring. A Solution to the Collapsing Problem

Carlos Caleiro and Jaime Ramos

Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice

David W. Miller

Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics

Arnon Avron, Jonathan Ben-Naim and Beata Konikowska

Aristotle’s Cubes and Consequential Implication

Claudio Pizzi

New Dimensions on Translations Between Logics

Walter A. Carnielli, Marcelo E. Coniglio and Itala M. L. D’Ottaviano

Posted by: John Baez on December 16, 2010 5:31 AM | Permalink | Reply to this

Re: A Global Glance on Categories in Logic

It seems Mathematische Annalen is temporarily open as well: http://www.springer.com/mathematics/journal/208.

Posted by: Chris Brav on December 16, 2010 8:28 PM | Permalink | Reply to this

Re: A Global Glance on Categories in Logic

Fun fact: This post has caused measurable effects. I received an email from the editor of Logica Universalis telling me that our “Global Glance” was the most downloaded math article in any Springer journal this week - you can see this at Springer’s real time toy page:

http://realtime.springer.com/journal/1661-8300

Posted by: Peter Arndt on December 19, 2010 1:50 PM | Permalink | Reply to this

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