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The theory of successor with an extra predicate

โœ Scribed by Wolfgang Thomas

Publisher
Springer
Year
1978
Tongue
English
Weight
734 KB
Volume
237
Category
Article
ISSN
0025-5831

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The Elementary Theory of Torsionfree Abelian Groups With a Predicate Specifying a Subgroup
โœ Peter H. Schmitt ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 367 KB ๐Ÿ‘ 1 views

This is proved by induction on 7n. For ni = 0 (\*) follows immediately from the definitions. Now take a E C,:,,, for m > 0. There is c E B,,,, such t'hat ac E pCp,n,-l + + C,,;f,l+l. There is thus a' E Cl~.flr-l with a E c + pa' + Cl,.,,f+l. By induction hypothesis a' E 6' + C,.,,, for some b' E @ B