Moosa, Rahim; Scanlon, Thomas Model theory of fields with free operators in characteristic zero. (English) Zbl 1338.03067 J. Math. Log. 14, No. 2, Article ID 1450009, 43 p. (2014). Summary: Generalizing and unifying the known theorems for difference and differential fields, it is shown that for every finite free algebra scheme \(\mathcal{D}\) over a field \(A\) of characteristic zero, the theory of \(\mathcal{D}\)-fields has a model companion \(\mathcal{D}\)-\(\text{CF}_{0}\) which is simple and satisfies the Zilber dichotomy for finite-dimensional minimal types. Cited in 2 ReviewsCited in 23 Documents MSC: 03C60 Model-theoretic algebra 12H05 Differential algebra 12H10 Difference algebra 12L12 Model theory of fields Keywords:canonical base property; difference field; differential field; generalised Hasse-Schmidt field; jet space; model companion; prolongation; simple theory; Zilber dichotomy PDFBibTeX XMLCite \textit{R. Moosa} and \textit{T. Scanlon}, J. Math. Log. 14, No. 2, Article ID 1450009, 43 p. (2014; Zbl 1338.03067) Full Text: DOI arXiv References: [1] DOI: 10.1007/BF01420277 · Zbl 0445.32021 · doi:10.1007/BF01420277 [2] DOI: 10.1090/S0002-9947-99-02498-8 · Zbl 0922.03054 · doi:10.1090/S0002-9947-99-02498-8 [3] DOI: 10.1112/S0024611502013576 · Zbl 1025.03026 · doi:10.1112/S0024611502013576 [4] DOI: 10.1007/978-1-4612-5350-1 · doi:10.1007/978-1-4612-5350-1 [5] Fujiki A., Nagoya Math. J. 85 pp 189– (1982) · Zbl 0445.32017 · doi:10.1017/S002776300001970X [6] DOI: 10.2307/2586538 · Zbl 0945.03051 · doi:10.2307/2586538 [7] DOI: 10.1016/S0168-0072(01)00096-3 · Zbl 0987.03036 · doi:10.1016/S0168-0072(01)00096-3 [8] Kamensky M., Int. Math. Res. Notices 24 pp 5571– (2013) [9] Matsumura H., Commutative Ring Theory (1986) · Zbl 0603.13001 [10] Moosa R., J. Reine Angew. Math. 620 pp 35– (2008) [11] DOI: 10.1017/S1474748010000010 · Zbl 1196.14008 · doi:10.1017/S1474748010000010 [12] Moosa R., Proc. London Math. Soc. (2011) [13] DOI: 10.1006/jabr.1997.7359 · Zbl 0922.12006 · doi:10.1006/jabr.1997.7359 [14] DOI: 10.1007/s00029-003-0339-1 · Zbl 1060.12003 · doi:10.1007/s00029-003-0339-1 [15] DOI: 10.2307/2695074 · Zbl 0977.03021 · doi:10.2307/2695074 [16] DOI: 10.2178/jsl/1045861515 · Zbl 1039.03031 · doi:10.2178/jsl/1045861515 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.