Modular arithmetic MA has the same axioms as first order Peano arithmetic except xSx0xSx0is replaced with xSx0xSx0 MA has finite models and every infinite model of MA must have nonstandard elements In Even XOR Odd Infinities I asked if every model of MA is exclusively even or exclusively odd I asked if this statement is a theorem of MA 1 xx0xx0xxx1xx0xx0xxx1 The answer was no Emil Jebek showed the 2adic integers Z2Z2 are a model of MA and the above
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