Abstract
In [7] the notion of Turing computable embeddings is introduced as an effective counterpart for Borel embeddings. The former allows for the study of classes of structures with universe a subset of ω. It also allows for finer distinctions, in particular, among classes with \(\aleph_0\) isomorphism types. The hierarchy of effective cardinalities that arises from TC embeddings has been studied, among other places, in [7] and [2]. In this work, we prove that the special class of ‘daisy graphs’, a subclass of undirected graphs used to code families of sets, has the same effective cardinality as the class of archimedian real closed fields. As a consequence, the class of abelian p-groups and the class of archimedian real closed fields are TC incomparable.
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Ocasio-González, V.A. (2012). Turing Computable Embeddings and Coding Families of Sets. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_54
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DOI: https://doi.org/10.1007/978-3-642-30870-3_54
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