AndresCaicedo - Network

By the way, the general result gives a silly proof that if \(a,b\) are positive integers, then \((a-1)(b-1)\ge0\):this is because \(a\cdot...

By the way, the general result gives a silly proof that if \(a,b\) are positive integers, then \((a-1)(b-1)\ge0\):

this is because \(a\cdot b\) has the partition property just described: any partition of an order of that length into two pieces either has the first piece of size at least \(a\), or the second piece of size at least \(b\), but \(a+b-1\) is the smallest number with that property.

The result depends on an instance of the pigeonhole principle: Given orders \(A,B\), write \(A\cdot B\) for the order resulting from...

The result depends on an instance of the pigeonhole principle:

Given orders \(A,B\), write \(A\cdot B\) for the order resulting from "taking \(B\) copies of \(A\)".

One can easily check that for any partition of \(A\cdot B\) in two pieces \(C,D\), either \(C\) contains a copy of \(A\), or else \(D\) contains a copy of \(B\).

This is completely general. And it is optimal when \(A=\omega\), the order of the natural numbers, and \(B=\omega^*\), its reversal.

Optimal means here that if an order \(L\) is such that, whenever \(L=C\cup D\), either \(C\) contains a copy of \(\omega\) or \(D\) contains a copy of \(\omega^*\), then \(L\) itself contains a copy of either \(\omega\cdot\omega^*\) or \(\omega^*\cdot\omega\).

I characterize all linear orders \(L\) such that any graph on \(L\) either contains (as an induced subgraph) a copy of the complete graph on...

I characterize all linear orders \(L\) such that any graph on \(L\) either contains (as an induced subgraph) a copy of the complete graph on the integers, or else it contains, for any \(n\), a set of \(n\) entirely unrelated vertices.

It is for an internal publication of the Universidad de los Andes, in Bogotá. They requested a small, somewhat expository piece, in...

It is for an internal publication of the Universidad de los Andes, in Bogotá. They requested a small, somewhat expository piece, in Spanish.

The result is new, though.

So I wrote a little paper.https://arxiv.org/abs/2503.15381

So I wrote a little paper.

https://arxiv.org/abs/2503.15381

I would most appreciate any alternatives to libgen you may suggest.Thanks.

I would most appreciate any alternatives to libgen you may suggest.

Thanks.

Found on Bluesky.https://www.sciencedirect.com/science/article/pii/S2210261224009209?via%3Dihub

Found on Bluesky.

https://www.sciencedirect.com/science/article/pii/S2210261224009209?via%3Dihub

@javier

@javier

Perpetual motion machine designs & theory (updated), by Nathan Coppedge.

Perpetual motion machine designs & theory (updated), by Nathan Coppedge.

Just got a message marked with "high importance" and sent to everybody in Math Reviews, which ends, in a very large font, withHave...

Just got a message marked with "high importance" and sent to everybody in Math Reviews, which ends, in a very large font, with

Have a SAFE holdiay WEEKEND!!!

I'll be giving a talk at Albion College on October 3rd, on "Fast growing functions". It is meant to be accessible to...

I'll be giving a talk at Albion College on October 3rd, on "Fast growing functions".

It is meant to be accessible to undergrads with no prior knowledge of mathematical logic, although it will touch on some results on provability.

http://mathcs.albion.edu/calendar.php#October%203,%202024

An archivist is looking at papers left on the old building, and he just found a copy of the workflow we used in the 80s.

An archivist is looking at papers left on the old building, and he just found a copy of the workflow we used in the 80s.

So, we moved. Literally across the street from the old building.

So, we moved. Literally across the street from the old building.

Math Reviews is moving in one week.

Math Reviews is moving in one week.

A tale of two footnotes. 1. Footnote 97, pg. 84.2. Footnote 83, pg. 148.From "a critical companion to Beowulf", by Andy Orchard.

A tale of two footnotes.
1. Footnote 97, pg. 84.
2. Footnote 83, pg. 148.

From "a critical companion to Beowulf", by Andy Orchard.

This is a very interesting topic, I wish I had more time to work on it.https://mathoverflow.net/q/476239/6085Richard Ketchersid and I proved...

This is a very interesting topic, I wish I had more time to work on it.

https://mathoverflow.net/q/476239/6085

Richard Ketchersid and I proved ages ago some results on cardinalities under determinacy, and some of our techniques (and a lot of hard work of others on the descriptive-set-theoretic side) should solve the explicit questions here, but the underlying thing is that we really know almost nothing about non-well-ordered cardinalities in (nice) models of determinacy.

Nooo...https://www.google.com/amp/s/www.cbsnews.com/amp/sanfrancisco/news/fire-damages-bookstore-in-rockridge-neighborhood-early-tuesday/This...

Nooo...

https://www.google.com/amp/s/www.cbsnews.com/amp/sanfrancisco/news/fire-damages-bookstore-in-rockridge-neighborhood-early-tuesday/

This is (was?) one of my favorite bookstores.

From https://mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts

From https://mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts

Man...(from Annals of Pure and Applied Logic, Volume 176, Issue 1, January 2025, 103497, "μ-clubs of Pκ(λ): Paradise in heaven"...

Man...

(from Annals of Pure and Applied Logic, Volume 176, Issue 1, January 2025, 103497, "μ-clubs of Pκ(λ): Paradise in heaven" by Pierre Matet. https://doi.org/10.1016/j.apal.2024.103497)