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Re: What's formal, axiomatic mathematics without the word "infinity"?

From Mikko <mikko.levanto@iki.fi>
Newsgroups sci.logic
Subject Re: What's formal, axiomatic mathematics without the word "infinity"?
Date 2023-06-20 11:10 +0300
Organization -
Message-ID <u6rmso$2d4ce$1@dont-email.me> (permalink)
References <f652ec1d-805e-41b3-af4c-3ac1d3b31603n@googlegroups.com>

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On 2023-06-19 05:50:57 +0000, Khong Dong said:

> https://qr.ae/pyPSmu

Ordinary formal first order logic does not define "infinity", and the
usual meaning of "infinity" is not definable there. Consequently,
ordinary first order theories don't and can't define "infinity". In
particular, the first order Peano arithmetic does not define "infinity".

In second and higher order logic it is possible to define "infinity".
That may also be possible in a non-standard extension of first order
logic.

Mikko

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Thread

What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-18 22:50 -0700
  Re: What's formal, axiomatic mathematics without the word "infinity"? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-19 06:58 -0700
    Re: What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-19 11:06 -0700
      Re: What's formal, axiomatic mathematics without the word "infinity"? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-19 19:02 -0700
  Re: What's formal, axiomatic mathematics without the word "infinity"? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-19 08:01 -0700
    Re: What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-19 17:24 -0700
      Re: What's formal, axiomatic mathematics without the word "infinity"? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-20 11:37 -0700
        Re: What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-20 11:57 -0700
          Re: What's formal, axiomatic mathematics without the word "infinity"? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-20 12:06 -0700
            Re: What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-20 12:12 -0700
              Re: What's formal, axiomatic mathematics without the word "infinity"? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-20 13:39 -0700
                Re: What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-20 15:33 -0700
  Re: What's formal, axiomatic mathematics without the word "infinity"? Mikko <mikko.levanto@iki.fi> - 2023-06-20 11:10 +0300
    Re: What's formal, axiomatic mathematics without the word "infinity"? Julio Di Egidio <julio@diegidio.name> - 2023-06-20 03:20 -0700
  Re: What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-20 10:19 -0700
    Re: What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-20 10:42 -0700
    Re: What's formal, axiomatic mathematics without the word "infinity"? Julio Di Egidio <julio@diegidio.name> - 2023-06-20 16:07 -0700
      Re: What's formal, axiomatic mathematics without the word "infinity"? Khong Dong <khongdongphong@gmail.com> - 2023-06-21 08:12 -0700
        Re: What's formal, axiomatic mathematics without the word "infinity"? Julio Di Egidio <julio@diegidio.name> - 2023-06-22 03:08 -0700

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