“Robinson's joint consistency theorem”的意思、由来-开放百科全书

词条

Robinson's joint consistency theorem

释义

References

Robinson's joint consistency theorem is an important theorem of mathematical logic. It is related to Craig interpolation and Beth definability.

The classical formulation of Robinson's joint consistency theorem is as follows:

Let and be first-order theories. If and are consistent and the intersection is complete (in the common language of and ), then the union is consistent. Note that a theory is complete if it decides every formula, i.e. either or .

Since the completeness assumption is quite hard to fulfill, there is a variant of the theorem:

Let and be first-order theories. If and are consistent and if there is no formula in the common language of and such that and , then the union is consistent.

References

{{cite book|last = Boolos|first = George S. |author2=Burgess, John P. |author3=Jeffrey, Richard C.|title = Computability and Logic|publisher = Cambridge University Press|date = 2002|pages = 264|isbn = 0-521-00758-5|url = https://books.google.com/books?id=Yy14JSjPyY8C}}

2 : Mathematical logic|Theorems in the foundations of mathematics

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。