Re: An example of a complete but undecidable theory

From: H. Enderton (hbe_at_sonia.math.ucla.edu)
Date: 08/26/04 

Date: Thu, 26 Aug 2004 17:22:27 +0000 (UTC)

Mike Oliver <mike_lists@verizon.net> wrote:
>So here's a question to which I don't know the answer off
>the top of my head: If T is decidable, is there a theory
>T' in some other language, such that T and T' are mutually
>relatively interpretable, and T' is complete? If so,
>then you might argue that a decidable theory is "morally"
>complete, except that its language is too rich, has too
>many symbols that T doesn't say enough about.

Let's take T to be the theory of equality, i.e., the set of
valid sentences in the language {=}. T is decidable, but
not complete.

Your move. What is T'?

--Herb Enderton

Relevant Pages

  • Re: Pupils to pay for illegal parking
    ... Then why use such intemperate and unmoderated language? ... get his head round. ... expressing themselves adequately for a wide variety of reasons, ... Penalty questioned by parent. ...
    (uk.legal)
  • Re: Pupils to pay for illegal parking
    ... But it's not irrelevant what language you said you used to your son. ... If you use intemperate language therefore, it's reasonable to assume that you are feeling pretty intemperate. ... If that's not encouraging him to treat the head with contempt I don't ... Penalty questioned by parent. ...
    (uk.legal)
  • Re: What does a single colon mean in a function title?
    ... try and get into actual programming using wxWidgets through ... wxDev-C++. ... language. ... Bet he has self inflated beyond the maximum pressure recommend for his head. ...
    (comp.lang.c)
  • Re: Qualia Question
    ... > define words in language any way you want. ... sense happening in our head - our thoughts etc), ... exist in an alternate universe (the universe of everything ... existence, when in fact, there is only one in our universe. ...
    (comp.ai.philosophy)
  • Re: Howto do the impossible with #define ?>?
    ... need them to argue about the fine points of a language, ... One would argue that 24 was the ... When a guy asks how to put out the fire on his head, ... unhelpful to the direct object of discourse? ...
    (comp.lang.c)