Please simply explain “extension by definitions” in logic

Asked Sep 30 '23 at 09:47

Active Sep 30 '23 at 10:27

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I am self learning logic and have come across the concept of “extension by definitions”. Unfortunately, Wikipedia has proved to be a bit unfriendly to my dysfunctional brain.

I understand the concept and idea behind it, just not the notational aspect. If anyone could walk me through the notation it would be a massive blessing. A specific example I am stuck on is the successor function and introducing constants other than 0 into the language of natural numbers. Thank you

edited Sep 30 '23 at 10:27

asked Sep 30 '23 at 09:47

Hasan Zaeem

2

Which course, textbook, or set of lecture notes are you following? Wikipedia should mostly serve as a reference but not as a didactic introduction to a beginner. – Benjamin Wang Sep 30 '23 at 09:59
I was using “a friendly i introduction to mathematical logic” by Leary, but they leave alot out and unexplained – Hasan Zaeem Sep 30 '23 at 10:02
Search on this site... in a nutshell, add a new predicate, relation, constant to the language through a def (a dedicated axiom) and prove that the "extended" theory does NOT prove new theorem not involving the newly defined terms wrt the original theory. – Mauro ALLEGRANZA Sep 30 '23 at 10:18
See this post as well as this one – Mauro ALLEGRANZA Oct 02 '23 at 06:38

Please simply explain “extension by definitions” in logic

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