Smullyan

I have just posted on my papers page a preprint of a review of

MR3379889
Smullyan, Raymond
Reflections—the magic, music and mathematics of Raymond Smullyan.
World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2015. x+213 pp.
ISBN: 978-981-4644-58-7; 978-981-4663-19-9

that I have submitted to Mathematical Reviews.

This entry was posted on Thursday, August 11th, 2016 at 6:00 am and is filed under Books, Incompleteness, math.HO, math.LO, MathReviews. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

Leave a Reply Cancel reply

Enter your comment here...

Fill in your details below or click an icon to log in:

Email (required) (Address never made public)

Name (required)

Website

You are commenting using your WordPress.com account. ( Log Out / Change )

You are commenting using your Twitter account. ( Log Out / Change )

You are commenting using your Facebook account. ( Log Out / Change )

Cancel

Connecting to %s

Categories

Mathoverflow

Answer by Andrés E. Caicedo for Continuum Hypothesis December 30, 2012

A classical reference is Hypothèse du Continu by Waclaw Sierpiński (1934), available through the Virtual Library of Science as part of the series Mathematical Monographs of the Institute of Mathematics of the Polish Academy of Sciences. Sierpiński discusses equivalences and consequences. The statements covered include examples from set theory, combinatorics, […]

Andrés E. Caicedo

Answer by Andrés E. Caicedo for Which journals publish expository work? October 25, 2013

There is a new journal of the European Mathematical Society that seems perfect for these articles: EMS Surveys in Mathematical Sciences. The description at the link reads: The EMS Surveys in Mathematical Sciences is dedicated to publishing authoritative surveys and high-level expositions in all areas of mathematical sciences. It is a peer-reviewed periodical […]

Andrés E. Caicedo

Answer by Andrés E. Caicedo for Does "$X \not\to (\omega)^\omega_2$ for every infinite $X$" imply ${\sf AC}$? March 29, 2022

The answer is no, the statement that for every set $X$ we have $$X\not\to(\omega)^\omega_2$$ does not imply the axiom of choice. This was shown by Kleinberg and Seiferas in 1973, see MR0340025 (49 #4782) Kleinberg, E. M.; Seiferas, J. I. Infinite exponent partition relations and well-ordered choice. J. Symbolic Logic 38 (1973), 299–308. https://doi.org/10.23 […]

Andrés E. Caicedo

On the structure of maximal Ramsey colorings October 25, 2021

For positive integers $a_1,\dots,a_n$, recall that the multicolor Ramsey number $R(a_1,\dots,a_n)$ is the smallest integer $N$ such that if the edges of the complete graph $K_N$ are colored with the $n$ colors $1,\dots,n$, then there is some $i\le n$ and a set of $a_i$ vertices, all of whose edges received color $i$. A maximal Ramsey$(a_1,\dots,a_n)$-colorin […]

Andrés E. Caicedo

Answer by Andrés E. Caicedo for How to rearrange only negative part of a conditionally convergent series to get any sum greater then initial? November 29, 2010

Georgii: Let me start with some brief remarks. In a series of three papers: a. Wacław Sierpiński, "Contribution à la théorie des séries divergentes", Comp. Rend. Soc. Sci. Varsovie 3 (1910) 89–93 (in Polish). b. Wacław Sierpiński, "Remarque sur la théorème de Riemann relatif aux séries semi-convergentes", Prac. Mat. Fiz. XXI (1910) 17–20 […]

Andrés E. Caicedo

Math.StackExchange

Answer by Andrés E. Caicedo for Are there examples of theorems proved via proper (i.e. non-conservative) extensions? May 7, 2013

Yes, this is a nice idea, and the approach is used in practice. I list four examples below, but there are many others. Any arithmetic statement, or any first order statement about $(\mathbb R,\mathbb N,+,\times,

Andrés E. Caicedo

Answer by Andrés E. Caicedo for If a function can only be defined implicitly does it have to be multivalued? June 4, 2011

Not necessarily. Consider the graph $G$ in ${\mathbb R}^2$ of the points $(x,y)$ such that $$ y^5+16y-32x^3+32x=0. $$ This example comes from the nice book "The implicit function theorem" by Krantz and Parks. Note that this is the graph of a function: Fix $x$, and let $F(y)=y^5+16y-32x^3+32x$. Then $F'(y)=5y^4+16>0$ so $F$ is strictly incre […]

Andrés E. Caicedo

Answer by Andrés E. Caicedo for Whether the map $x\mapsto x^3$ in a finite field is bijective August 20, 2013

Following Tomas's suggestion, I am posting this as an answer: I encountered this problem while directing a Master's thesis two years ago, and again (in a different setting) with another thesis last year. I seem to recall that I somehow got to this while reading slides of a talk by Paul Pollack. Anyway, I like to deduce the results asked in the prob […]

Andrés E. Caicedo

Answer by Andrés E. Caicedo for Is it possible to formalize the idea that large cardinal axioms don't limit us, while their negations do? November 25, 2013

One way we formalize this "limitation" idea is via interpretative power. John Steel describes this approach carefully in several places, so you may want to read what he says, in particular at Solomon Feferman, Harvey M. Friedman, Penelope Maddy, and John R. Steel. Does mathematics need new axioms?, The Bulletin of Symbolic Logic, 6 (4), (2000), 401 […]

Andrés E. Caicedo

Answer by Andrés E. Caicedo for Is $6.12345678910111213141516171819202122\ldots$ transcendental? March 5, 2011

This is a transcendental number, in fact one of the best known ones, it is $6+$ Champernowne's number. Kurt Mahler was first to show that the number is transcendental, a proof can be found on his "Lectures on Diophantine approximations", available through Project Euclid. The argument (as typical in this area) consists in analyzing the rate at […]

Andrés E. Caicedo

	Is there a Borel-mea… on 414/514 Examples of Baire clas…
	Simple bijectiveness… on 580 -Some choiceless results…
	Schur’s theore… on 580 -III. Partition calcu…
	Uncountable linearly… on 403/503 – Homework …
	What is a non-constr… on On strong measure zero se…
	function from Nmathb… on Hindsight
	Cauchy Schwarz Inequ… on 275 -Positive polynomials
	What is a Cantor-sty… on 580 -Some choiceless results…
	Question about Gener… on 580 -Some choiceless results…
	Set has Measure Zero… on On strong measure zero se…
	Non-measurable subse… on 580 -Cardinal arithmetic …
	hmeng1 on 414/514 The theorems of Rieman…
	580 -Cardinal arithm… on 580 -Cardinal arithmetic …
	580 -Cardinal arithm… on 580 -Cardinal arithmetic …
	580 -Cardinal arithm… on 580 -Cardinal arithmetic …

A kind of library

Smullyan

Leave a Reply Cancel reply

Categories

Recent Comments

Mathematical links

My pages

Others

Mathoverflow

Math.StackExchange

Archives

A kind of library

Smullyan

Share this:

Like this:

Related

Leave a Reply Cancel reply

Categories

Recent Comments

Mathematical links

My pages

Others

Mathoverflow

Math.StackExchange

Archives