Math Forum / Mathematics / Mathematical Logic / July 2006

As we all know, it was comrade Stalin's brilliant and objective article
_Marxism and linguistics_ in 1951 (IIRC) that established conclusively
that language is not a part of the superstructure, and hence formal
logic is a legitimate non-ideological discipline. I'm wondering ...

Hello everyone. There are some things that are unclear to me about the
fascinating Busy Beaver sequence.
I will explain my reasoning, and please correct me if I made any
mistake.

http://web.lemoyne.edu/~giunta/Clausius.html
http://www.mdpi.org/lin/clausius/clausius.htm
Rudolf Clausius, Ueber die bewegende Kraft der Wärme, Annalen der
Physik und Chemie, 79, 368-97, 500-24 (1850):

Theorem.Set theory ZFC is inconsistent.
The proof of it the unexpected fact, leans on that standard assumption
(SA), that:  set of all formulas of the canonical set theory ZFC is an
infinite   countable ZFC-set.

Nothing can be 'too numerous to count'. Either it is counted or it is
not. There is no 'numerous' middle road. Take as example the infinite
series, e.g. 1,2,3,4, ...
Here, the injunction "and so on", or,  " ..." ,  as it is popularly

Pleese help me prove the following:
Let S be a structure, while S* is a substructure of S, that's definable
in S by a first order formula. Prove that if the theory of S* is
undecidable, then the theory of S is undecidable as well.

Can someone give me some advice on this problem. I have no ideas on how
to even start it.
Let A_n be arbitrary subsets of omega for every n in omega. Prove that
there is some subset B of omega such that A_n is turing reducible to B

dans sci.logic,soc.history.science
<KI2xg.24060$cO7.9846@reader1.news.jippii.net>
aatu perlenspiel:
 As we all know, it was comrade Stalin's

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Could someone help me understand this problem:
Let L be a language containing (at least) a binary predicate symbol <.
Let [gothic A] be an L-structure such that < is a linear order of A.
Prove that [gothic A} has an elementary extension [gothic B] such that

Is (R \ 0, <) an elementary substructure of (R, <), where R represents
the reals?
I think so for the mere purpose that (Q \ 0, <) is an elementary
substructure of (Q, <), where Q represents the rationals. So shouldn't

Curing ulcers, IBS, CROHNS, DEPRESSION, ANXIETY, SCHIZOPHRENIA,
CANCER...?
I heard about your mothers suffering from Ulcers and bring forth the
following logical possibility that relates to a great many other

Pentcho Valev wrote:

Dirk van Dalen's book Logic and Structure (4th edition) p.188 gives "a
slightly changed AI-rule" (where A is the universal quantifier), in words
the rule says: from a formula F you can derive Ax F[x/y], where y does not
occur free in F or in a hypothesis of the derivation of F, and ...

Let L and L' be languages such that L' = L U {c}, where c is a constant
symbol not in L.
What is the difference between these two statements:
(1) T' is a finitely axiomatizable theory of L', and T = T' [intersect]