A method of existential interpretation was introduced in [2]. It allows proving undecidability of modest strata of many first order theories. Here we improve the method and its presentation, strengthen somewhat the previous results and prove a couple of new results. The reader is not supposed to be acquainted with [2].Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46063/1/153_2005_Article_BF02297651.pd
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